theorem
  x is being_a_product_of_squares & y is being_an_amalgam_of_squares
  implies x*y is being_an_amalgam_of_squares
proof
  assume that
A1: x is being_a_product_of_squares and
A2: y is being_an_amalgam_of_squares;
  x is being_an_amalgam_of_squares by A1,Lm19;
  hence thesis by A2,Lm86;
end;
